What is the Least Common Multiple of 37680 and 37695?

Least common multiple or lowest common denominator (lcd) can be calculated in two way; with the LCM formula calculation of greatest common factor (GCF), or multiplying the prime factors with the highest exponent factor.

Least Common Multiple of 37680 and 37695 with GCF Formula

The formula of LCM is LCM(a,b) = ( a × b) / GCF(a,b).
We need to calculate greatest common factor 37680 and 37695, than apply into the LCM equation.

GCF(37680,37695) = 15
LCM(37680,37695) = ( 37680 × 37695) / 15
LCM(37680,37695) = 1420347600 / 15
LCM(37680,37695) = 94689840

Least Common Multiple (LCM) of 37680 and 37695 with Primes

Least common multiple can be found by multiplying the highest exponent prime factors of 37680 and 37695. First we will calculate the prime factors of 37680 and 37695.

Prime Factorization of 37680

Prime Factorization of 37695

Now multiplying the highest exponent prime factors to calculate the LCM of 37680 and 37695.

LCM(37680,37695) = 2⁴ × 3¹ × 5¹ × 157¹ × 7¹ × 359¹
LCM(37680,37695) = 94689840